The noted agitator looks to help the Rangers secure a postseason berth and eliminate the rival New York Islanders from playoff contention when the teams meet on Tuesday.
Avery had two goals and completed a "Gordie Howe Hat Trick" of a goal, an assist and a fight on Sunday to lead the Rangers (41-29-9) to a 7-2 rout of Toronto - one of the teams behind them in the Eastern Conference playoff race.
"I was definitely nervous this afternoon," Avery said. "I didn't think I was going to get a couple of goals or anything like that, I just wanted to come out and really play well and try and be a difference."
The five-year veteran has done just that since the Rangers acquired him from Los Angeles in a five-player trade on Feb. 5. The Rangers are 16-5-5 with Avery in the lineup after going 25-24-4 before his arrival.
The left wing's tenacious play and 19 points since the deal have helped the Rangers move into sixth place in the East, four points ahead of ninth-place Toronto with three games remaining.
"I think he was the biggest factor in our season lately," Rangers captain Jaromir Jagr said. "Once he came here, he changed everything. We got a great player who can score goals, play rough, play tough. He's tough to play against."
The Rangers are in position to return to the playoffs for a second straight season for the first time since a four-season run that started with a Stanley Cup championship in 1993-94. They made the playoffs in 2005-06, but lost their last five games of the regular season before being swept by New Jersey in the first round.
The Islanders (36-30-6), meanwhile, are on the verge of missing the playoffs for the second straight season. They are four points back of eighth-place Montreal with four games left, and a regulation loss in this game coupled with a Canadiens' victory over Boston on Tuesday would eliminate them from postseason contention.
The Islanders have lost four straight, including a 5-2 defeat at home to Ottawa on Saturday. Wade Dubielewicz made 41 saves in his first start of the season in place of Rick DiPietro, who has been sidelined with post-concussion syndrome since a 2-1 overtime loss to the Rangers on March 25.
"I thought Dubie played as well as he could," Islanders coach Ted Nolan said. "He was the only one who gave us a chance. Every team loses people to injuries. It doesn't mean you can feel sorry for yourself.
"We have to have some heart. We lost Ricky and (Chris) Simon and we feel sorry for ourselves. It doesn't mean you can mail it in and not try."
The Rangers have won three straight in this series, including two in a row at Nassau Coliseum, after dropping the first four meetings of the season. Henrik Lundqvist has been in net for the last three victories, posting a 0.95 goals-against average in those contests.
Lundqvist is 7-0-0 with a 1.70 GAA and two shutouts in his last eight starts overall.